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3 years ago

Which expression is equivalent to -8?

Mathematics

1 answer:

torisob [31]3 years ago

7 0

2/8 I think....:| :|○~○

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D^2(y)/(dx^2)-16*k*y=9.6e^(4x) + 30e^x

MA_775_DIABLO [31]

The solution depends on the value of $k$ . To make things simple, assume $k>0$ . The homogeneous part of the equation is

$\dfrac{\mathrm d^2y}{\mathrm dx^2}-16ky=0$

and has characteristic equation

$r^2-16k=0\implies r=\pm4\sqrt k$

which admits the characteristic solution $y_c=C_1e^{-4\sqrt kx}+C_2e^{4\sqrt kx}$ .

For the solution to the nonhomogeneous equation, a reasonable guess for the particular solution might be $y_p=ae^{4x}+be^x$ . Then

$\dfrac{\mathrm d^2y_p}{\mathrm dx^2}=16ae^{4x}+be^x$

So you have

$16ae^{4x}+be^x-16k(ae^{4x}+be^x)=9.6e^{4x}+30e^x$
$(16a-16ka)e^{4x}+(b-16kb)e^x=9.6e^{4x}+30e^x$

This means

$16a(1-k)=9.6\implies a=\dfrac3{5(1-k)}$
$b(1-16k)=30\implies b=\dfrac{30}{1-16k}$

and so the general solution would be

$y=C_1e^{-4\sqrt kx}+C_2e^{4\sqrt kx}+\dfrac3{5(1-k)}e^{4x}+\dfrac{30}{1-16k}e^x$

8 0

2 years ago

A secret code is made up of three digits followed by

kari74 [83]

Most likely 10 because the initial amount is 5

5 0

2 years ago

According to a poll, 80% of California adults (403 out of 506 surveyed) feel that education is one of the top issues facing Cali

fiasKO [112]

f(h(x))= 2x -21

Step-by-step explanation:

f(x)= x^3 - 6

h(x)=\sqrt[3]{2x-15}

WE need to find f(h(x)), use composition of functions

Plug in h(x)

f(h(x))=f(\sqrt[3]{2x-15})

Now we plug in f(x) in f(x)

f(h(x))=f(\sqrt[3]{2x-15})=(\sqrt[3]{2x-15})^3 - 6

cube and cube root will get cancelled

f(h(x))= 2x-15 -6= 2 x-21

6 0

2 years ago

I need help!!!! I don’t understand and it’s very confusing

irga5000 [103]

Answer:

Step-by-step explanation:

I explained in my last answer but someone deleted it

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2 years ago

You want to save $500 for a trip to Legoland you have planned in 6 months. Which inequality shows the least amount you must save

sladkih [1.3K]

Answer:

6x ≥ 500

Step-by-step explanation:

I took the test but also it means that in six months, you have to save that amount of money to get exactly or more than 500, so this would be the correct answer!

7 0

2 years ago